Coding Exercise on Derivatives

Problem statement

Given the function $f(x) = x^2+ \sin(x^{1/2}) + \log(x) + \exp(\cos(x))$, calculate its second-order derivative, i.e., $\frac{\partial^2}{\partial^2 x} f(x)$, at the point $x = x_0$. Your implementation should use PyTorch's torch.autograd.grad() utility for calculating derivatives.

To calculate second-order derivatives, you first need to calculate the first-order derivative $\frac{\partial f(x)}{\partial x}$ and then differentiate it again with respect to $x$. In other words,